Simpson opened the scoring for Wasps
Wasps 38 (28)
Tries: Simpson, Varndell, Jacobs, Waldouck Con: Walder 3. Pens: Walder 4
Glasgow 26 (13)
Tries: Jackson, Hall Cons: Harley, Jackson Pen: Jackson 4.
Scrum-half Joe Simpson's brilliant early try helped Wasps pick up their first victory of the Heineken Cup campaign at the expense of Glasgow.
The Man of the Match picked up the play from a scrum near the Glasgow 22 and powered over at the corner.
Tom Varndell, Ben Jacobs and Dominic Waldouck also scored tries and Walder kicked 18 points, as Wasps collected a bonus point.
Ruaridh Jackson was Glasgow's main contributor, with 19 points.
After Simpson had given Wasps the lead, Walder missed the subsequent conversion and a penalty before finally hitting the target after Jackson had got Glasgow off the mark.
Worse was to follow for Glasgow when prop Moray Low was sin-binned for hands in the ruck and Walder punished them with the subsequent kick.
Varndell was next to touch down for Wasps, when he collected a grubber kick from Walder and outpaced DTH Van der Merwe.
But Glasgow hit back through Jackson, who picked up a chip from flanker John Barclay and went over.
Jackson's conversion and penalty reduced the deficit to 18-13 before Walder slotted over a penalty and centre Jacobs jinked his way over from close range to give Wasps breathing space.
The sides exchanged penalties in the opening moments of the second 40 before Wasps added a bonus point thanks to a try from substitute Waldouck.
England star Riki Flutey found flanker Dan Ward-Smith who fed the ball to Waldouck, who was unstoppable.
Glasgow kept the match alive when Henry Pyrgos passed out of the tackle to Dougie Hall who went over, but they were unable to secure a losing bonus point as the Wasps defence held firm to the whistle.
Wasps' rugby director Tony Hanks:
"We're rapt. It puts us in a better position in the pool. This was a huge game that we had to win to stay in the pool.
"If you look at all the other pools and scenarios they're all quite tight. You can't afford to be none from two at this point."
Glasgow coach Sean Lineen:
"We had a poor first 20 minutes collectively. They weren't doing anything special and we were hanging off them.
"The tries were too soft. We showed more spirit in the second half and scored a couple of tries ourselves."
London Wasps: Richard Haughton, Tom Varndell, Ben Jacobs, Riki Flutey, David Lemi, Dave Walder, Joe Simpson, Charlie Beech, Rob Webber, Zak Taulafo, Simon Shaw, Richard Birkett, Dan Ward-Smith, Tom Rees (capt), Andy Powell.
Replacements: Joe Ward, Shaun Ruwers, Ben Broster, Marty Veale, Joe Worsley, Nic Berry, Dominic Waldouck, Mark Van Gisbergen.
Glasgow Warriors: Bernardo Stortoni, DTH van der Merwe, Max Evans, Graeme Morrison, Federico Aramburu, Ruaridh Jackson, Colin Gregor, Jon Welsh, Fergus Thomson, Moray Low, Tom Ryder, Richie Gray, Robert Harley, John Barclay (capt), Richie Vernon.
Replacements: Dougie Hall, Ryan Grant, Ed Kalman, Ryan Wilson, Calum Forrester, Henry Pyrgos, Duncan Weir, Rob Dewey.